Equation 677 Database

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Magma bf0a60561efc…

magma bf0a60561efc
Size
705
Isomorphism class hash
bf0a60561efc4448f5e0160dd82ed3f1cd0504e8e78113e08300af95921e4288
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 18:23:56
Display reorder
660,66,648,647,657,649,67,617,608,607,609,68,637,628,627,629,69,568,567,577,569,70,588,587,597,589,71,548,547,557,549,468,467,64,477,469,428,427,65,435,429,448,447,63,457,449,527,528,60,537,529,487,488,61,497,489,507,508,62,517,509,698,702,685,694,38,640,652,641,651,36,600,601,612,611,37,621,620,632,631,41,561,572,560,571,39,581,592,580,591,40,541,552,540,551,461,472,44,460,471,421,432,42,422,431,441,452,43,440,451,532,520,47,521,531,492,481,45,480,491,512,500,46,501,511,686,689,701,692,59,275,258,132,359,57,133,273,259,357,58,134,274,260,358,55,271,261,135,355,56,272,262,136,356,54,270,263,137,354,266,256,50,138,350,264,257,48,139,348,265,255,49,140,349,252,269,53,141,353,253,267,51,142,351,254,268,52,143,352,680,668,677,669,14,323,2,79,204,12,80,321,1,205,13,78,322,0,206,17,319,5,82,207,15,320,3,83,208,16,318,4,81,209,314,8,20,77,210,312,6,18,75,211,313,7,19,76,212,11,317,23,73,213,9,315,21,74,214,10,316,22,72,215,664,674,665,672,244,655,656,654,642,245,614,615,616,602,243,634,635,636,622,240,575,576,574,562,241,595,596,594,582,242,555,556,554,542,475,476,250,474,462,434,439,251,438,437,455,456,249,454,442,536,535,246,534,522,496,495,247,494,482,516,515,248,514,502,699,687,697,688,197,659,650,653,643,195,613,619,610,603,196,633,639,630,623,193,579,570,573,563,194,599,590,593,583,192,559,550,553,543,479,470,203,473,463,420,430,201,433,423,459,450,202,453,443,530,539,199,533,523,490,499,200,493,483,510,519,198,513,503,693,704,695,703,182,644,646,645,658,180,605,604,606,618,181,625,624,626,638,185,564,566,565,578,183,584,586,585,598,184,544,546,545,558,464,466,188,465,478,424,426,186,425,436,444,446,187,445,458,526,524,191,525,538,486,484,189,485,498,506,504,190,505,518,696,700,690,691,93,100,335,419,32,94,417,101,333,30,95,418,99,334,31,92,96,331,415,35,90,97,332,416,33,91,98,330,414,34,106,326,84,410,27,107,324,85,408,28,105,325,86,409,29,329,102,87,413,26,327,103,88,411,24,328,104,89,412,25,684,681,662,666,130,347,154,168,371,131,169,345,155,369,129,170,346,153,370,126,343,150,171,367,127,344,151,172,368,128,342,152,173,366,338,145,121,174,362,336,146,122,175,360,337,144,120,176,361,148,341,124,177,365,149,339,125,178,363,147,340,123,179,364,678,673,667,683,226,292,279,383,311,227,381,293,280,309,225,382,291,281,310,222,288,278,379,307,223,289,276,380,308,224,290,277,378,306,298,285,217,374,302,299,286,218,372,300,297,287,216,373,301,284,294,220,377,305,282,295,221,375,303,283,296,219,376,304,675,663,670,661,119,157,407,235,395,117,236,158,405,393,118,234,156,406,394,115,160,403,238,391,116,161,404,239,392,114,159,402,237,390,163,398,110,233,386,164,396,108,231,384,162,397,109,232,385,401,166,113,229,389,399,167,111,230,387,400,165,112,228,388,671,676,682,679 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 11, B) with E = magma#82788998f5140702896c545961cafeebe136162a04e08140ecf7d45fe0422a3d, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 45.

last edited by qawbecrdtey at 2026-10-03 18:23:57 · history